Applying the Boussinesq approximation [1]} to the mass balance equations results in the density difference only appearing in the buoyancy term. The mass balance equations are
\( \mathbf {u}^{*}+\mathbf {\kappa }\left(\nabla p^{*}+{\mathbf {y}}\left(\rho -\rho _{0}\right) g\right)=0,\) 
